Finite Group Databasebeta

← #21425535

Subgroups — #21425535

Order 7552.

256 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273658C211yesmaximal, characteristic, complemented
2C2×(C2×D59)⋊C8C211yesmaximal, characteristic
3#16837259C211yesmaximal, characteristic
4#16837259C211yesmaximal, characteristic
5#16837165C211yesmaximal, characteristic, complemented
6#16837164C211yesmaximal, characteristic, complemented
7C59×#340C211yesmaximal, characteristic, complemented
8C22×C4×D59C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×(C2×D59)⋊C4—21no—
13C2×(C2×D59)⋊C4—21no—
14#14273658—22no—
15(C2×D59)⋊C8—22no—
16C59⋊#95—21no—
17C59⋊#95—21no—
18C22×C8×C59C2211yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21C23×D59D411yescharacteristic
22C22×C4×C59—21no—
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—21no—
26C22×Dic59—21no—
27C22×Dic59D411yescharacteristic
28C2×C4×D59—21no—
29C2×C4×D59—21no—
30C2×C4×D59—21no—
31C2×C4×D59—21no—
32C2×C4×D59—21no—
33C2×C4×D59—21no—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41(C2×D59)⋊C4—42no—
42(C2×D59)⋊C4—42no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8D412yes—
50C23×C59C2×D411yescharacteristic
51C22×D59—21no—
52C22×D59—21no—
53C22×D59—21no—
54C22×D59—21no—
55C22×D59—21no—
56C22×D59—21no—
57C22×D59SD1612yes—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C2×C4×C59#4111yescharacteristic
67C2×C4×C59#4111yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C2×Dic59—21no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C4×D59—41no—
80C4×D59—41no—
81C4×D59—41no—
82C4×D59—41no—
83C8×C59—41no—
84C59⋊C8—22no—
85C22×C59#12111yescharacteristic
86C22×C59#12311yescharacteristic
87C22×C59#12311yescharacteristic
88C22×C59C2×SD1611yescharacteristic
89C22×C59#13511yescharacteristic
90C22×C59AGL(1,ℤ/8)11yescharacteristic
91C22×C59#13711yescharacteristic
92C2×D59—22no—
93C2×D59—22no—
94C2×D59—22no—
95C2×D59—41no—
96C2×D59—41no—
97C2×D59—41no—
98C2×D59—41no—
99C4×C59—81no—
100C4×C59—81no—
101C4×C59#12311yescharacteristic
102C4×C59#12411yescharacteristic
103C4×C59#12611yescharacteristic
104C4×C59#12611yescharacteristic
105Dic59—41no—
106Dic59—81no—
107Dic59—81no—
108#2077—591nomaximal, Sylow
109C2×C59#39711yescharacteristic
110C2×C59#46511yescharacteristic
111C2×C59#46811yescharacteristic
112C2×C59#48111yescharacteristic
113C2×C59#48211yescharacteristic
114C2×C59#48311yescharacteristic
115C2×C59#48511yescharacteristic
116D59—42no—
117C2×#106—591no—
118C2×C22⋊C8—591no—
119#380—591no—
120#380—591no—
121#340—591no—
122#340—591no—
123#340D5911yescharacteristic, complemented
124C59#207711yescharacteristic, complemented, Sylow
125C23×C4—591no—
126C22×C8—591no—
127C22×C8C2×D5911yescharacteristic
128C2×C4⋊C4—591no—
129C2×C4⋊C4—591no—
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C4⋊C4C2×D5911yescharacteristic
132C2×C22⋊C4—1181no—
133C2×C22⋊C4—1181no—
134#106—1182no—
135C22⋊C8—1182no—
136#95—1181no—
137#95—1181no—
138C24—591no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—591no—
142C22×C4—1181no—
143C22×C4—1181no—
144C22×C4—1181no—
145C22×C4—1181no—
146C22×C4—1181no—
147C22×C4—1181no—
148C22×C4—1181no—
149C22×C4—1181no—
150C22×C4C22×D5911yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—592no—
155C2×C8—1181no—
156C2×C8—1181no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1181no—
162C4⋊C4—1181no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C22⋊C4—2362no—
166C22⋊C4—2362no—
167C23—592no—
168C23—1181no—
169C23—1181no—
170C23—1181no—
171C23—1181no—
172C23—1181no—
173C23—1181no—
174C23D4×D5911yescharacteristic
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1181no—
182C2×C4—1181no—
183C2×C4—1181no—
184C2×C4—2361no—
185C2×C4—2361no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4—2361no—
189C2×C4—2361no—
190C2×C4—2361no—
191C2×C4—2361no—
192C2×C4—2361no—
193C2×C4—2361no—
194C2×C4#1174568511yescharacteristic
195C2×C4#1174568511yescharacteristic
196C2×C4#1174568511yescharacteristic
197C2×C4D4×D5911yescharacteristic
198C2×C4#1174568711yescharacteristic
199C2×C4#1174568911yescharacteristic
200C8—41no—
201C8—1182no—
202C22—1182no—
203C22—1182no—
204C22—1182no—
205C22—2361no—
206C22—2361no—
207C22—2361no—
208C22—2361no—
209C22#1427370011yescharacteristic
210C22#1427370911yescharacteristic
211C22#1427371211yescharacteristic
212C22SD16×D5911yescharacteristic
213C22#1427375011yescharacteristic
214C22#1427375111yescharacteristic
215C22#1427375611yescharacteristic
216C4—81no—
217C4—81no—
218C4—4721no—
219C4—4721no—
220C4—2361no—
221C4#1427371211yescharacteristic
222C4#1427371311yescharacteristic
223C4#1427372111yescharacteristic
224C4#1427372211yescharacteristic
225C2—2362no—
226C2#1683733111yescharacteristic
227C2#1683763411yescharacteristic
228C2#1683764711yescharacteristic
229C2#1683771911yescharacteristic
230C2#1683772911yescharacteristic
231C2#1683773411yescharacteristic
232C2#1683774211yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#2077
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14273658C2semidirect
5. #16837165C2semidirect
6. #16837164C2semidirect
7. C59×#340C2semidirect
123. #340D59semidirect
124. C59#2077semidirect